The principal Lyapunov exponent of a dynamical system is a natural measure of the instability of the system. In our work, we computed the supremum of the principal Lyapunov exponent associated to the system dy/dt = A(t)y, y∈R^2, where the function A ranges in L^∞_loc([0,+∞);{A1,A2}), A1,A2∈R^(2x2). This kind of dynamical systems, where the dynamics can be discontinuous with respect to the time variable, are known in literature as switched systems. This computation is reduced to an optimal control problem. Applying Pontryagin Maximum Principle (PMP) to this problem, we were able to find all controls satisfying necessary conditions prescribed by PMP and then we found among them the optimal one. This is a joint work with A. A. Agrachev.